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Zbl 1204.39028
Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces.
(English)
[J] Appl. Math. Lett. 23, No. 10, 1198-1202 (2010). ISSN 0893-9659

Let $G$ be an additive group and $X$ a complete non-Archimedean normed space. Let the function $f: G \to X$ satisfy the functional equation $$f(x+2y)+f(x-2y) = 4( f(x+y)+f(x-y)) -24f(y) - 6f(x) + 3f(2y)$$ for all $x, y \in G$. In this paper, the authors study the Hyers-Ulam-Rassias stability of the above functional equation in non-Archimedean spaces.
[Prasanna Sahoo (Louisville)]
MSC 2000:
*39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains

Keywords: functional equation; non-Archimedean normed spaces; mixed type cubic-quartic functional equation; additive group; Hyers-Ulam-Rassias stability

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